In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both (▼×)2 and (▼×)4 operators. The element has a very small number of degrees of freedom, and it imposes the inter-element continuity along the tangential direction which is appropriate for the approximation of magnetic fields. We also provide explicit formulae of basis functions for this element.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics